Moving Charges In Magnetic and Electric Fields Electromagnetism Moving Charges In Magnetic and Electric Fields

Magnetic Forces – Charged Particles I. Charged particles in external magnetic fields a charged particle in motion, induces a magnetic field around the particle which is perpendicular to the motion of the particle

induced magnetic field around a particle interacts with the external magnetic field the induced magnetic field arrow is attracted toward the south and north poles of the magnets resulting in a downward force.

Below the particle, the induced and external magnetic fields repel one another to create a downward force. The result of a charged particle going through a magnetic field: particle will be deflected by a force which is perpendicular to both the original direction of the particle's motion and the external magnetic field.

Magnitude of the deflecting force The deflecting force on a charged particle moving through an external magnetic field is calculated using: | Fm| = q v B sin θ where: Fm = deflecting force from the magnetic field (N) B =magnetic flux density or magnetic field strength (Tesla) (T) q = charge of moving particle (C) v = speed of particle (m/s) θ = angle between v and B Note: The maximum deflecting force will occur when θ= 90o. Thus sin 90o= 1 and Fm= qvB.

Example: A 20 g particle with a charge of +2.0 C enters 0.20 T a magnetic field at 90o to the field. If the speed of the particle is 40 m/s, what is the acceleration that is experienced by the particle in the diagram below?

An alpha particle enters a 50 T field at 30°to the field at a speed of 500 m/s. What is the magnitude of the deflecting force experienced by the alpha particle? (An α+2 particle has a charge of 2 x 1.60 x 10-19C = 3.2 x 10-19C.)

Applications of Magnetic Forces a. Mass spectrometer www.edumedia-sciences.com/en/a105-mass-spectrometer http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/MassSpec/masspec1.htm

b. Van Allen radiation belts

c. Black and white television http://www.colorado.edu/physics/2000/tv/big_picture.html

The Movement of Charges Through Electric and Magnetic Fields Simultaneously -when a charge passes through a magnetic field which is perpendicular to an electric field, it can pass through undeflected when no deflection of the charge occurs, the magnetic force is equal to the electrical force

When the forces are equal, (Fm = Fe) the speed of the charge can be determined Fm is down by 3rd LHR when e is in B Fe is up, e is attracted to the positive plate When Fe up = Fm down, e passes E and B undeflected Speed of electron can be determined

Example Eg) An electron enters a magnetic field of 2.00 x 10 -3 T at 90 degrees. An electric field of 1000 N/C is perpendicular to the magnetic field. Determine the kinetic energy of the electron as it passes undeflected between the two fields.

Current Balance -when a current carrying wire is positioned perpendicular to B, the current in the wire can be adjusted to equal the force of gravity downwards with the magnetic force upwards. This is referred to as current balance where Fg downwards equals Fm upwards.

Example: Eg) A 6.00 m length of wire is to a magnetic field of If the mass of the wire in the magnetic field is 15.0 g, what current must pass through the wire to suspend it?